The scope is a 14" Tscopes of circa 2004 vintage. The mirror in question is an Obsidian Lite 14" which is made of plate glass, about 1" thick and weighs around 10lbs.
The mirror cell is a 6 point flotation with 4 corner pegs/retaining clips:

As you can see, there doesn't appear to be any sling or edge support system and the mirror appears supported by the 4 corner pegs only:
(TScopes website stock photo)

On my scope, the corner pegs are padded by a firm rubbery layer at least 5mm thick.

So the main question:
1. Do you folks think this is enough support or does there need to be some sort of sling or wire support?

2. Will the fact that the mirror is being supported only by the bottom 2 pegs when horizontal cause damage to the mirror?

With a mirror that thin, I would actually be more worried about the 6 points on back. From the tables here it looks like 6 points is just on the edge of acceptable for a 12" mirror 1" thick, so you might want to step up to an 18 point for yours.

Actually, your 6 point cell is okay. The site shows examples of 13.1" x 1" plate glass as well as 16 "x 0.875" plate glass. You would like to have PV distortions less than about 1/20th wave. The 16" is pushing things a bit. I've used a similar support with my 14" x 1" plate glass mirror and it works fine. If you don't notice any astigmatism at high mags and various viewing angles don't sweat it.

After looking at this a bit, I think I can explain what's going on (having made the mirror ). Keep in mind I've never seen one of these scopes in the flesh.

Ed at TScopes made 9 point cells for these mirrors, for a while I had a sample of one such "triangle", which was simply a thick piece of Baltic birch with the pivot point indicated and 3 nylon screws at the positions more or less indicated in the attached picture, where I've merged PLOP output for such a cell (variable angles selected) with a keystone corrected version of your cell picture.

What it looks to me that somebody did is to replace the inner ring of supports with cork or felt pads. Or perhaps all of them, some of which fell off. In any case all 9 points should have the same support profile for the cell to work properly.

The edge support is fine for these mirrors, as designed and implemented.

PLOP returns support figures of 2nm RMS surface for this cell, which should be more than adequate, given that all the mirrors were made to a 1/8th wave PV error envelope. The cell theoretically delivers 1/30th wave PV support.

Thanks everyone for your opinions, especially for Mark, who is the mirror maker.
Now I'm rest assured I can go ahead and install the mirror, when work and family allow. I'm looking forward to first lighting this scope and Mark's exceptional mirror Looking at the test data for the Tscopes series of 14", there's a small chance my mirror could turn out to be a "lemon". However that "lemon" tested out at 1/8th wave and 0.94 Strehl, so I'd say that makes not just lemonade but outright lemon candy for correcting low sugar levels... (i.e. pretty sweet!)

I would comment that the top corner stops are unnecessary in an alt-az dob configuration. They should definitely NOT touch the mirror and the mirror should only rest on the bottom two points.Because the scope may be transported with the mirror in place, it's OK to have a top "safety clip" that overhangs the mirror slightly to keep the mirror from sliding out of the holder, but this should not touch the mirror at all in use in the field.